block-coordinate algorithm – Optimization Online

A Class of Randomized Primal-Dual Algorithms for Distributed Optimization

Published: 2014/06/24, Updated: 2014/10/25

Convex Optimization, Nonsmooth Optimization, Stochastic Programming block-coordinate algorithm, convex optimization, distributed algorithm, monotone operator, preconditioning, primal-dual algorithms, stochastic quasi fejér sequence

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide array of monotone inclusion problems. These methods rely on a sweep of blocks of variables which are activated at each iteration according to a random rule, … Read more

Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping

Published: 2014/04/29, Updated: 2014/05/27

Patrick L. Combettes

Jean-Christophe Pesquet

Convex Optimization, Nonsmooth Optimization, Stochastic Programming averaged nonexpansive operator, block-coordinate algorithm, douglas-rachford algorithm, fixed point algorithm, forward-backward algorithm, primal-dual operator splitting, stochastic quasi fejér sequence, structured minimization problem

This work investigates the properties of stochastic quasi-Fejér monotone sequences in Hilbert spaces and emphasizes their pertinence in the study of the convergence of block-coordinate fixed point methods. The iterative methods under investigation feature random sweeping rules to select the blocks of variables that are activated over the course of the iterations and allow for … Read more